Inkjet devices, such as printers, are configured to print an image onto a substrate, such as paper, plastic, or other material. Inkjet devices generally include a print head that ejects ink droplets selectively from nozzles on the print head onto the substrate, also referred to as “inkjetting.” The ink droplets deposit on the substrate and a desired image is printed.
Inkjetting is a complex phenomenon involving several different physical processes interacting together. There are a variety of types of inkjet devices that use different mechanisms for inkjetting. For example, inkjet devices may include print heads using mechanisms such as piezoelectric, thermal, electrohydrodynamic, and other suitable mechanisms. Piezoelectric inkjets use a piezoelectric element to acoustically excite ink in a channel behind the nozzle. The resulting changes in pressure at the nozzle cause droplets to eject. The piezoelectric element is operated by actuation waveforms, which are short electrical pulses generated for each ejection of a droplet.
For piezoelectric inkjets, the pressure at the orifice is based on a pressure waveform, which is typically a sequence of voltage ramps and plateaus on the order of approximately 1-100 volts (V) and approximately 1-100 microseconds (μs) in duration. Each time the voltage changes, the piezoelectric element deforms, which initiates acoustic pressure waves that travel to the nozzle and to the fluid reservoir. When the pressure waves reach the nozzle, the resulting changes in pressure control the dynamics of the fluid at the nozzle, which may result in the formation of a fluid column that ejects into one or more droplets from the nozzle.
When the ink stream breaks up into droplets, it may result in a series of uniform large droplets that are each separated by one or more much smaller droplets referred to as “satellites.” The shape of the pressure waveform determines the fluid dynamics at the nozzle, which determine multiple characteristics of the fluid droplets, such as the droplet volume and velocity and the satellite volume and size. It is difficult to correlate the pressure waveform and resulting droplet formation and velocity.
The pressure waveform may vary based on the particular implementation. A standard pressure waveform is the unipolar waveform that consists of two rising and falling impulses in sequence. The unipolar waveform is parameterized by the peak voltage and the dwell time, which is the time elapsed between the pulses. For a particular fluid and inkjet, an optimal dwell time for a unipolar waveform exists when the ejected droplet momentum is maximized at a given voltage.
Other pressure waveforms may be utilized based on the goals of a particular implementation. For example, reducing droplet volume may require advanced waveforms to induce complex pressure gradients at the orifice. Additionally, fluids with challenging rheological properties may be prone to unstable jetting and may not be jettable with the standard unipolar waveform.
Multiple methods have been proposed and utilized to improve piezoelectric inkjets, which may include optimizing droplet volumes. Many of these methods provide for the inclusion of non-dimensional numbers and may also vary the pressure waveform, such as by using a bipolar waveform with modifications to dwell times. Numbers proposed and used in some methods include the Ohnesorge number, a related Z number, and/or other ratios. Such numbers relate to the jettability and/or printability of a particular fluid with a particular inkjet. Limits are often proposed for the numbers based on different fluids, such as wax suspensions or low viscosity inks, and the structure of inkjet nozzles, such as orifice radius, orifice length, or orifice diameter. The limits have taken into account fluid parameters such as fluid viscosity, viscous dissipation, fluid surface tension, fluid density and/or the formation of satellites.
With respect to varied pressure waveforms, often a manual trial-and-error process is performed to select the optimal waveform. For fluids and performance requirements that fall into typical operating conditions for an inkjet device, a simple unipolar waveform may be easily optimized for stable jetting. However, in order to jet fluids with challenging properties, while specifying droplet resolution, requires increasingly complex waveforms. As the complexity of the waveform increases, its versatility increases but the dimensionality of the problem explodes. While multiphysics simulations and models may predict droplet formation, these models are extremely complex, non-linear, application-specific, excessively time consuming, and are non-invertible in nature. Furthermore, no analytic models exist that are useful for predicting droplet volumes from actuation waveforms. Additionally, any waveform tuning is specific to that particular combination of fluid and inkjet device.
The challenge of methods using non-dimensional numbers and/or varied waveforms is that the methods may be too conservative, e.g., artificially confine the limits of jetting performance. These methods also may depend on the fluid rheology and inkjet device geometry, without taking into account the complex coupling between the piezo-structural materials, actuation dynamics, inkjet geometry and fluid rheology. Manual tuning, as stated above, is only limited to simple waveforms with few parameters. Accordingly, a need has arisen to automatically optimize complex pressure waveforms to control droplet resolution while maintaining placement accuracy for any combination of material and inkjet device.